The IPC-property (“inductive limit product commutation property”) is a technical condition on a category $A$ which ensures that presheaves with values in $A$ have a good notion of sheafification.
A category $A$ is said to satisfy the IPC-property if
for
every family $\{I_s\}_{s \in S}$ of small filtered categories
and for any family $\{\alpha_s : I_s \to A\}$ of functors
indexed by a small set $S$
the canonical morphism
is an isomorphism.
The IPC property is definition 3.1.10 in
It is invoked for sheafification in section 17.4 there.
Last revised on December 31, 2023 at 19:25:58. See the history of this page for a list of all contributions to it.